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The Spanish world number one showed no mercy to 28th seed Damir Dzumhur on Margaret Court Arena, as he rediscovers his best form after ankle trouble.
The top seed raced through the match in just 1hr 50min, wasting as little energy as possible in the 6-1, 6-3, 6-1 rout.
“I was very, very focused,” Nadal said. “I’m very happy with everything and to have another chance on Sunday.”
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Third seed Dimitrov, who could meet Nadal in the semis, had plenty to prove after a huge second-round fright from a qualifier, who pushed him to five sets.
And the Bulgarian delivered in a testing 6-3, 4-6, 6-4, 6-4 win over Russian rising star Andrey Rublev as temperatures touched 40 Celsius (104 Fahrenheit).
“These are the most important matches for me, when things are not working for me and I find a way,” he said. “I’m feeling good physically, the heat didn’t scare me at all today, so that’s a good sign.”
He will next face the winner of an intriguing night match which pits Australian Nick Kyrgios against French veteran Jo- Wilfried Tsonga.
Fourth seed Svitolina also kept her title dreams alive by ending the hopes of young teenage pretender Marta Kostyuk.
“She’s definitely got a bright future,” said Svitolina, adding: “It’s very special for me to get past the third round.”
She next plays another qualifier — big-serving Czech Denisa Allertova who romped past Magda Linette 6-1, 6-4 — for a place in the quarter-finals on Sunday.
In a tournament shorn of seeds, 81st ranked Petra Martic also swept into the round of 16, celebrating her 27th birthday by holding off a gritty three-set challenge from Thai qualifier Luksika Kumkhum.
Her reward is a match against Belgium’s Elise Mertens, who beat struggling Alize Cornet of France in two tough sets.
Cornet was among players wilting in the heat, with a doctor taking her blood pressure early in the second set as she succumbed to the baking weather.
No matches have been called off or roofs closed at the opening Grand Slam of the year despite the soaring temperatures, with tournament organiser Craig Tiley defending the decision.
“These are professional athletes,” he said.
“We are at the end of the day an outdoor event. We want it to stay an outdoor event as long as possible but at the same time ensuring that the health and wellbeing of players is taken care of.”
Organisers only activate the extreme heat policy when the temperature exceeds 40 Celsius and the wet bulb globe temperature index hits 32.5 Celsius.
On Thursday, Novak Djokovic described the conditions as “brutal”, complaining it was hard to breathe.
Kyle Edmund joined Nadal in the round of 16, overcoming the elements in a fighting five-set win over Nikoloz Basilashvili and will next play Italian Andreas Seppi who won a battle of the veterans against Croatia’s 38-year-old Ivo Karlovic.
Spanish 10th seed Pablo Carreno Busta, a semi-finalist at last year’s US Open, also marched on.
Despite being the second seed, Caroline Wozniacki has not impressed so far.
She is the late match on Rod Laver Arena against Dutch 30th seed Kiki Bertens and will play 19th-seeded Slovak Magdalena Rybarikova if she wins.